A 48 kg skier skis directly down a frictionless slope angled at 5° to the horizontal. Assume the skier moves in the negative direction of an x axis along the slope. A wind force with component Fx acts on the skier.
(a) What is Fx if the magnitude of the skier's velocity is constant?
(b) What is Fx if the magnitude of the skier's velocity is increasing at a rate of 1.0 m/s2?
N
(c) What is Fx if the magnitude of the skier's velocity is increasing at a rate of 2.0 m/s2?
N
test
To solve these problems, we need to apply Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration.
In this scenario, the skier is experiencing a force due to the wind acting along the direction of motion (horizontal), which we'll denote as Fx.
(a) Since the magnitude of the skier's velocity is constant, it means that the skier is neither accelerating nor decelerating. Therefore, the net force acting on the skier must be zero.
Net force (Fx) = 0 N
(b) If the magnitude of the skier's velocity is increasing at a rate of 1.0 m/s^2, it means that the skier is experiencing an acceleration of 1.0 m/s^2 in the direction of motion. To find the net force, we can use Newton's second law.
Net force (Fx) = mass (m) × acceleration (a)
In this case, the mass of the skier is given as 48 kg. Therefore,
Fx = 48 kg × 1.0 m/s^2
Fx = 48 N
The wind force component Fx is equal to 48 N.
(c) If the magnitude of the skier's velocity is increasing at a rate of 2.0 m/s^2, it means that the skier is experiencing an acceleration of 2.0 m/s^2 in the direction of motion. Using Newton's second law, we can calculate the net force.
Fx = 48 kg × 2.0 m/s^2
Fx = 96 N
The wind force component Fx is equal to 96 N.